Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations

Jehanzeb Chaudhry; Zachary Stevens

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arXiv · 2206.02905

Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations

Jehanzeb Chaudhry·Zachary Stevens

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Abstract

We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical MLMC algorithms that use either a hierarchy of uniform meshes or adaptively refined meshes based on Richardson extrapolation, and employ a stopping criteria that relies on assumptions on the convergence rate of the MLMC levels. This work develops two adaptive refinement strategies for the MLMC algorithm. These strategies are based on a decomposition of an error estimate of the MLMC bias and utilize variational analysis, adjoint problems and computable residuals.

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Jehanzeb Chaudhry, Zachary Stevens. 2022-06-06. Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations. https://arxiv.org/abs/2206.02905

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